Pinning of diffusional patterns by non-uniform curvature
Name
1901.09900.pdf
Description
Accepted version
Size
3.39 MB
Format
Unknown
Checksum (MD5)
6ee1d808b0815e29e5f49592f46e6798
Author(s)
Frank, John R
Guven, Jemal
Kardar, Mehran
Shackleton, Henry
Date Issued
2019
Journal
EPL (Europhysics Letters)
Publisher
IOP Publishing
Version
Author's final manuscript
Abstract
© 2019 EPLA. Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational symmetry. Deformations, e.g., by a bulge or indentation, break symmetry and can pin a pattern. We adapt methods of conformal mapping and perturbation theory to examine how curvature inhomogeneities select and pin patterns, and confirm the results numerically. The theory provides an analogy to quantum mechanics in a geometry-dependent potential and yields intuitive implications for cell membranes, tissues, thin films, and noise-induced quasipatterns.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1209/0295-5075/127/48001
